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- Title
An approach based on Haar wavelet for the approximation of fractional calculus with application to initial and boundary value problems.
- Authors
Mehandiratta, Vaibhav; Mehra, Mani; Leugering, Günter
- Abstract
In this paper, we propose the numerical approximation of fractional initial and boundary value problems using Haar wavelets. In contrast to the Haar wavelet methods available in literature, where the fractional derivative of the function is approximated using the Haar basis, we approximate the function and its classical derivatives using Haar basis functions. Moreover, error bounds in the approximation of fractional integrals and the fractional derivatives are derived, which depend on the index J of the approximation space VJ and the fractional order α. A neural network problem modeled by a system of nonlinear fractional differential equations is also solved using the proposed method. The numerical results show that the proposed numerical approach is efficient.
- Subjects
BOUNDARY value problems; INITIAL value problems; HAAR function; FRACTIONAL differential equations; NONLINEAR differential equations; FRACTIONAL calculus
- Publication
Mathematical Methods in the Applied Sciences, 2021, Vol 44, Issue 4, p3195
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.6800